Magnetic Field Noise from High Permeability Magnetic Shields for Precision Measurements

High permeability magnetic shields often generate magnetic field noise that can limit the sensitivity of precision measurements. We show that calculations based on the fluctuation-dissipation theorem allow evaluation of magnetic field noise, either by current or spin fluctuations, from high permeability metals and ferrites over a broad frequency range. For example, the noise spectrum of a mu-metal shield generally exhibits three distinct frequency dependent behaviors: low frequency 1/f spin noise, white noise due to Johnson noise current, and high frequency roll-off due to self-shielding. To reduce the effect of Johnson noise current, we built a multi-layer shield for a potassium SERF atomic magnetometer using ferrite for the innermost layer. We found that the white noise was reduced from about 20 fT/Hz$^{1/2}$, as expected for an all-mu metal shield, to 0.75 fT/Hz$^{1/2}$, limited by laser noise. The low frequency 1/f noise agreed well with calculation based on the measured complex permeability of the ferrite. Our method can be used to identify low noise shielding materials for further suppression of shield-generated noise for compact atomic magnetometers.